Griese was born in Evansville, Indiana to Ida (Ulrich) and Sylverious "Slick" Griese. Slick owned a plumbing company in Evansville and died in 1955 when Bob was ten years old. Bob played baseball primarily, and excelled as a pitcher. He also starred in basketball and football at Evansville's Rex Mundi High School. He earned 12 varsity letters for the Monarchs.

He led his American Legion baseball team to the American League Baseball World Series in the summer of 1963; Funkhouser Post #8 did not reach the finals, as the Arthur L. Peterson Post of Long Beach, California won the title.[1]

He led the basketball team to the No. 1 ranking in Indiana during the 1962–63 season and a record of 19–3. He scored 900 points in his high school career and while being named All-Sectional, he could not lead the Monarchs past Evansville Bosse in the highly competitive Evansville IHSAA Sectional.[2]

The Monarchs were 15–5 during his Junior (9–1) and Senior (6–4) seasons, as he was named 1st Team All-City for three seasons.[2][3] After being recruited by several colleges for football, Bob chose Purdue, where he majored in business management and became a three-sport star.[4] In 1984, Bob was inducted into the Indiana Football Hall of Fame.[5]

While at Purdue, Bob became a member of Sigma Chi Fraternity. In college Griese pitched for the baseball team, going 12-1 one season, played guard on the basketball team, and played quarterback, kicker, and punter for the Purdue football team. There were many games where Griese scored every one of Purdue's points. He currently[when?] ranks #9 in scoring at Purdue; #5 in scoring among non-kickers and #4 among kickers.[6] Griese’s passing skills greatly improved under the tutelage of head coach Jack Mollenkopf and quarterback coach Bob DeMoss.

In his junior year at game against the top-ranked Notre Dame, Griese completed 19 of 22 passes as he led the Boilermakers to an upset win.[7]

His sterling college career earned him induction into the College Football Hall of Fame in 1984. Purdue did not have a practice of retiring numbers and instead, he was inducted as an inaugural member of the Purdue Intercollegiate Athletic Hall of Fame in 1994.[11]

Griese was the fourth player selected in the 1967 Common Draft. He was selected by the AFL's Miami Dolphins. Griese recorded 2,005 yards and 15 touchdowns in his rookie year in Miami.

An AFL All-Star during his first two years, Griese went on to earn AFL All-Star or AFC-NFC Pro Bowl honors in six more seasons. While he never put up huge numbers, his leadership played an important role in helping the Dolphins compete in three consecutive Super Bowls, winning the latter two contests.

Griese started the season as the team’s second-string quarterback behind John Stofa. However, Stofa broke his ankle in the first quarter of the first game of the 1967 season (after Joe Auer missed a block on a linebacker), and Griese stepped in and went on to a 35-21 victory against the Denver Broncos. Coincidentally, Griese's first play in the pros was a touchdown pass to Joe Auer. The next three years were fairly rough for the expansion team Dolphins. The wins were hard to come by, and after a difficult 1969 season that seemed to be a step back from the 1968 season, coach George Wilson was fired.

Dolphin owner Joe Robbie brought in Don Shula from the Baltimore Colts in 1970, and immediately the Dolphins' personality and fortunes turned. The team found a new discipline, and discovered what it took to become a winning football team. They went from a 3-10-1 team in 1969 to a 10-4 team in 1970, making the playoffs. The next year the team made it to the Super Bowl, and Bob Griese was named the Most Valuable Player in the NFL, receiving the Jim Thorpe trophy. Although the Dolphins lost that Super Bowl in a bitter loss to the Dallas Cowboys, there was no denying that this was a team that was quickly becoming a powerhouse.

The next season began well, with the Dolphins winning their first few games over their toughest opponents of the year. However, in the fifth game of the season, Bob Griese was tackled by Deacon Jones and Ron East of the San Diego Chargers, and he went down with a broken leg and dislocated ankle. In came Earl Morrall, fresh off the waiver wire from Shula’s former team, the Baltimore Colts. Morrall guided the Dolphins through the rest of the regular season, and maintained an unbeaten record in the process. Morrall even led the AFC in passing, as Griese had done the previous year. However, as the playoffs began, it was obvious that the Dolphins were not as strong as they needed to be to last very long in the postseason. The Dolphins barely squeaked by a Cleveland Browns team that they should have beaten easily, and then they got a slow start the following week against the Pittsburgh Steelers. Shula knew that he needed to turn back to Griese to relieve the ailing Morrall. Shula simply turned to Bob at halftime and asked him, “Are you ready?” to Griese’s reply, “Yes, I’m ready.” With that, Bob took the field and responded as if he had never been away, leading the Dolphins to a convincing win and their second straight Super Bowl appearance.

Despite their unbeaten season, the Dolphins were listed as two point underdogs to the Washington Redskins in Super Bowl VII. However, true to the form of the season, the Dolphins played a perfect, ball control game. Griese connected on 8 of 11 passes for 88 yards and a touchdown, as Larry Csonka rushed for over 120 yards, and the Dolphins defense, led by 17 tackles by Manny Fernandez, stymied the Redskin offense. Washington's only score was on a blocked kick, and Miami won 14-7.

The following year, the Dolphins seemed even more efficient and dominant. Although they did not make it through the season undefeated, they again easily marched to the Super Bowl, and then totally dominated the Minnesota Vikings in Super Bowl VIII, winning 24-7.

In 1975, Griese and the Dolphins had another strong season. But late in the season in a game against the Baltimore Colts, Griese suffered a broken toe and was out for the rest of the season. The Dolphins finished 10-4, and missed out on the playoffs for the first time in the Shula era. In 1976, the Dolphins were beset with many injuries, and the team finished with a 6-8 record, the first time Don Shula had ever suffered a losing season in his career (which went back to 1963).

1977 was a rebound year for both Griese and the Dolphins. Bob began to wear eyeglasses on the field.[12] On Thanksgiving, 1977, Griese threw six touchdown passes in three quarters to defeat the St. Louis Cardinals 55-14.[13] Bob again led the AFC in touchdown passes thrown but the Dolphins rebound to a 10-4 record was again not enough to get the team into the playoffs.

The following year, Bob tore ligaments in his knee in a preseason game. However, when he came back, he was just as strong a passer as he had been the previous year. In one game against the Houston Oilers, Griese dueled with Oiler running back Earl Campbell in an offensive slugfest. Griese threw for over 300 yards and Campbell rushed for nearly 200. The Oilers won the game 35-30. For the year, Griese completed a league leading 63% of his passes, as the Dolphins went 11-5, losing again to the Oilers in the playoffs.

In 1979, Bob suffered from some nagging leg injuries that affected his throwing. He was not as effective, and he began to hear some criticism. However, he was able to lead the Dolphins to a 10-6 record. The Dolphins then found themselves dominated by the Pittsburgh Steelers in the first round of the playoffs.

In 1980, Griese had found that he had lost his starting spot in the roster to either Don Strock or rookie David Woodley. However, Griese came off the bench for several games in a row to lead comeback wins. Griese won back the starting spot in the fifth game of the season, but was tackled hard by Mike Ozdowski of the Baltimore Colts. The tackle tore up Bob’s shoulder, and he was out for the rest of the year. The injury eventually led to Griese’s decision to retire from the game at the age of 35. Bob was eventually elected to the Pro Football Hall of Fame in 1990.

He had established his reputation as the “Thinking Man’s Quarterback,” as he brilliantly called his own plays throughout his career. Dolphin owner Joe Robbie called him “the cornerstone of the franchise,” around whom the Miami Dolphins were built. Robbie elected to ask Griese to stay on for another year as assistant coach, which he did for the 1981 season, helping Strock and the young Woodley as they teamed to become the famous “Woodstrock.” Bob decided that he did not like the hours required to be an assistant coach, hoping to devote more time to his family, yet still enjoyed being part of the game. (Sources for Pro Football Career found in Undefeated, by Bob Griese, 2000, and The Winning Edge by Don Shula, 1974.)

The Miami Dolphins had the highest winning percentage in all professional sports in the 1970s, and Bob Griese was its starting quarterback throughout the decade, except when he was injured for several games in 1972, 1975, and 1978.

In Griese's 14 pro seasons, he threw for 25,092 yards and 192 touchdowns. Griese also rushed for 994 yards and seven scores. Griese was a six-time Dolphins' MVP and was All-Pro in 1971 and 1977. He played in two AFL All-Star games and six Pro Bowls.

The Dolphins retired his number 12 during a Monday Night Football game in 1985, telecast on ABC, the network which would prominently be featured in his post-football career.

To stay in touch with the game, Griese decided to take a job as an announcer for NBC Sports, teaming with Charlie Jones for NFL games. Later, Griese was hired by ABC Sports, where he began to provide color commentary for college football games. He formed a memorable team with Keith Jackson, and found many opportunities to watch his son Brian Griese play for the Michigan Wolverines. Eventually, Bob was considered one of the top commentators in the country. ABC was at first reluctant to let Griese broadcast Michigan games, fearing a conflict of interest. But when they decided to give it a try, Bob remained as impartial and professional as he could be, even referring to his son as “Griese,” rather than Brian, and pointing out errors when he felt necessary.

On January 1, 1998, Bob got to broadcast the Rose Bowl game, the last college game of his son's career. Brian was named MVP of the game, leading his Wolverines to an undefeated season and the national championship title with their Rose Bowl victory. Bob and Brian were emotional at that moment, as they thought of Bob’s wife Judi, who had died from breast cancer in 1988 but whom they both felt was there at that special moment. Bob and Brian later wrote a book, entitled Undefeated (ISBN 0-7852-7021-3), which discussed not only their football connection, but also their love for Judi. (That book is the source of this information.) Brian became a professional quarterback and broadcaster himself, playing for the Denver Broncos and Tampa Bay Buccaneers, and later commentating games for ESPN and ABC.

Griese married Purdue classmate Judi Lassus in June 1967,[20] following their graduation, and they had three sons. A nurse, she lost a six-year battle with breast cancer at age 44 in early 1988.[21][22] He now resides with his second wife, Shay, in Jupiter, Florida, and Banner Elk, North Carolina. His youngest son is Brian Griese (b. 1975), who also played quarterback in the NFL. In 2006, he was on Wheel of Fortune. Griese won, and the winnings went to Judi's House.